you want to buy a $218,000 home. you plan to pay 10% as a down payment, and take out a 30 - year loan for…

Explanation:

Step1: Calculate loan amount

The home price is $218000. The down - payment is 10% of the home price. So the loan amount $L$ is $(1 - 0.10)\times218000$. $L=(1 - 0.10)\times218000=0.9\times218000 = 196200$

Step2: Calculate monthly payment formula

The formula for the monthly payment $M$ of a loan is $M = P\times\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P$ is the principal loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. For a 30 - year loan, $n = 30\times12=360$ months.

Case b: 6% interest rate

The annual interest rate $i = 6%=0.06$, so the monthly interest rate $r=\frac{0.06}{12}=0.005$. The principal $P = 196200$. $M_b=196200\times\frac{0.005(1 + 0.005)^{360}}{(1 + 0.005)^{360}-1}$ First, calculate $(1 + 0.005)^{360}\approx6.022575$. $M_b=196200\times\frac{0.005\times6.022575}{6.022575 - 1}$ $M_b=196200\times\frac{0.030112875}{5.022575}\approx1176.04$

Case c: 7% interest rate

The annual interest rate $i = 7%=0.07$, so the monthly interest rate $r=\frac{0.07}{12}\approx0.005833$. The principal $P = 196200$. $M_c=196200\times\frac{0.005833(1 + 0.005833)^{360}}{(1 + 0.005833)^{360}-1}$ First, calculate $(1 + 0.005833)^{360}\approx7.039988$. $M_c=196200\times\frac{0.005833\times7.039988}{7.039988 - 1}$ $M_c=196200\times\frac{0.041014}{6.039988}\approx1331.48$

Answer:

a) $196200 b) $1176.04 c) $1331.48